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Verizon Wireless has announced, via its Chief Financial Officer Fran Shammo, that it sold 4.2M iPhone units in the fourth quarter of 2011. This doubled sales from Q3 and then some.

The sales increased Verizon’s gross margins to 600 basis points, she told attendees at a Citigroup Inc. event in San Francisco today. The company couldn’t even fill all of its orders before the year was out and ended up with a backlog of 120,000 iPhone orders yet to fill.

Unfortunately, the numbers aren’t all positive. Verizon heavily subsidizes devices to onboard users, then makes up its outlay over time as those users continue to pay their contract fees. This results in the estimation that Verizon’s fourth quarter should show a decline of 6% in the company’s profit margins. The margins are expected to drop to around 42% from 47.8% in the third quarter.

The sales of 4.2M phones in Q4 brings it “extremely close” to meeting its target of 11 million iPhone sales in 2011, said Shammo.